Answer: 121.5√3 ft² ≈ 210.4 ft²
Step-by-step explanation:
Area of shaded region = Area of entire hexagon - Area of inside hexagon
Area of regular hexagon = [tex]\dfrac{3\sqrt3}{2}\ a^2[/tex] where a is the side length
[tex]Area_{\ entire\ hexagon}=\dfrac{3\sqrt3}{2}\ (6\sqrt3)^2\\\\.\qquad \qquad \qquad \qquad =\dfrac{3\sqrt3}{2}\cdot 108\\\\.\qquad \qquad \qquad \qquad =3\sqrt3\cdot 54\\\\.\qquad \qquad \qquad \qquad =162\sqrt3\\\\\\Area_{\ inside\ hexagon}=\dfrac{3\sqrt3}{2}\ (3\sqrt3)^2\\\\.\qquad \qquad \qquad \qquad =\dfrac{3\sqrt3}{2}\cdot 27\\\\.\qquad \qquad \qquad \qquad =\dfrac{81\sqrt3}{2}\\\\.\qquad \qquad \qquad \qquad =40.5\sqrt3[/tex]
[tex]Area_{\ shaded\ region}=162\sqrt3-40.5\sqrt3\\\\.\qquad \qquad \qquad \qquad =\boxed{121.5\sqrt3}[/tex]
